Post-tensioned slab applicabilty 5

[gcfreem]

Under what circumstances is it appropriate/efficient to use post-tensioning for an elevated (i.e. not slab on grade) concrete slab? Specifically, I am desiging a storage building with column spacing of either 20' or 30' in each direction. I don't have experience with post-tensioned slabs, but my feeling is that it may not be appropriate for the heavy live loads (125 psf) of a storage building. Thanks.

 

[rapt]

Everyone,
This will become obvious below but we must distinguish between FEM analysis and software that produces reinforcement/prestress requirements based on FEM analysis. All FEM produces is a set of stresses which, when convereted to moments, describe the moments on the floor system that have to be designed for.
A tacked on design program then designs reinforcement. FEM does not produce reinforcement drawings, someones interpretation of FEM results does, whether it be done manually or by computer.

1 FEM vs EFM: There is no difference in the overall moment over a panel width between the 2. This can be easily verfied by setting up a simple square grid of columns in FEM and the same EFM sample and comparing the results. The whole thing should add up to wL^2/8 in each direction (same as for EFM) for a uniform load. If it does not, change FEM programs because the one you are using is WRONG.

The difference is that FEM tells us the distribution of thre moments across the slab based on elastic analysis while with EFM we have to guess the distribution based on experience, eg 75/25 for maximum negative moment and 60/40 or 55/45 for maximum positive moments and varying between.
Both methods should give the same total area of reinforcement over the width of a panel. There is no saving using FEM.
If software tells you there is a difference, question it because it is wrong. For example, if an FEM program allows for Mxy moments in the analysis and then ignores them in design (as several prominant ones do), then the difference will be at least 15% and possibly up to 25% UNDER estimation of the reinforcement requirements. This does not mean that you can use 15-25% less reinforcement, it means it has underdesigned by 15-25%.
It does not mean that FEM is wrong. FEM is reporting Mx, My and Mxy. It means that the design application tacked onto the end of the FEM is wrong because the developer does not understand design using FEM, or they are trying to cheat (hopefully it is the first but either is worrying).

2 I have no problem with EFM. It is how I design most times. What I do have a problem with is the assumption that the design moment on a PT flat slab is a total moment spread over the total width of a panel.

In RC design, ACI tells us to distribute the moments between column and middle strips in different propertions depending on whether it is at support or mid span. This fairly closely models the results of an FEM distribution of moments and I agree entirely with it.

In PT design ACI tells us to use the total moment over the total panel width (resulting in an average moment and averaged stresses over the entire width of the panel). This is blatently incorrect.

2--1 As I explained in earlier posts, for flat slabs where the tendons and reinforcement are placed in a pattern that provides a load path to the supports, it is possible to do the ultimate strength calculation the ACI way and work out a total capacity over the width of a panel rather than dividing into column and middle strips. The justification of this comes back to a yield line solution and the slab will stand up.
The 2 generally accepted tendon patterns for this are
1 a column/middle strip pattern in each direction with about 70% of the tendons in the coilumn strip and 30% in the middle strip in each direction - result is similar to the FEM moment result and the elastic response of the slab
2 a banded/distributed pattern with tendons equally spaced in one direction and concentrated over the columns in the other direction - result is a one way failure pattern completely different to the FEM moment result and to the elastic response of the slab
3 a third solution is similar to 1 but the ratios in each direction are varied but still consistent with each other. In this scenario, solution 2 is one extreme of the solutions possible.

In all cases, all of the laod is carried in each direction and there is a load path to the supports in the reinforcement pattern.

This yield line solution is only possible however when tendon layouts as described above are used, loads are uniform, concrete cross-section is uniform and the slab is uncracked at service - see below.

Otherwise solution 1 must be used where the tendon layout matches the elastic moment response of the slab.

2--2 The real problem with the ACI method arises when we come to serviceability design, crack control and deflections.
Concrete cracks based on the stresses at each point in the section, not based on the average stress over a 10m (33') width of slab. A Crack in concrete can only be restrained by reinforcement that crosses the crack. Sounds logical and obvious. But that is not the way ACI works for PT slabs.

The slab cracks based on the elastic moment pattern, not some assumed ultimate failure criterion. It keeps cracking as load is increased until the final ultimate capacity of the slab matches the reinforcement pattern. If that pattern is banded/distributed, then a lot of cracking and redistribution and extra deflection have to occur to achieve the final ultimate capacity.

What we are interested in is the first cracking and that is dependent on the elastic moments and their distribution across the floor panel. ACI ignores this.

Even though 75% of the moment is in only half of the width at the supports, ACI allows you to assume it is spread evenly. This means that you are grossly underestimating the actual stress which will crack the concrete. So ACI designers are assuming slabs are uncracked for cracking and deflection calculations when they are actually cracked. This is very unconservative. Add in the fact that everyone ignores restraing stresses and your software might be ignoring Mxy (15% of the moemnts) and your slabs will be a lot more cracked than you expect and deflections will be much higher.

The further serviceability problem is that banded/distributed slabs cannot be allowed to crack at service unless crack control reinforcememt, calculated based on the requiremnents of all areas of the slab for their actual stresses, is supplied based on the elastic moment pattern not the failure pattern. The decision on this cracking must be based on the elastic stress pattern and allow for restraing stresses due to shrinkage and temperature change.

 

[haynewp]

JAE,

I have not used FEM for a slab before, in fact, it has been a while since I have even done an EFM. But I do remember that wl^2/8 total moment (positive reinforcing + negative reinforcing for a slab panel in either direction has to add up to wl^2/8) as rapt was talking about to make sure there is a minimum amount of reinforcing required for the slab. Again, the wl^2/8 must apply for EACH direction so you are reinforcing it for that load twice but this is required.

I think this total moment in each direction goes back to a guy name Nichols around 1915 that proved this and changed the way slabs were reinforced. I remember reading that 2 way type slabs were almost all under-designed prior to this guy showing this total moment requirement. The EFM is supposed to be derived from Nichols' analysis. The Nichols' analysis looks at the entire moment in a slab panel.

Regarding PT slabs and serviceability cracking, I really haven't heard of PT slabs designed in the U.S. performing all that poorly either when designed based on EFM. But I do not specialize in just doing one thing all the time (ex. PT concrete slabs) so I am not constantly exposed to designing and inspecting only prestressed slab systems. So maybe I am wrong. Apply carpet as necessary.

 

[hokie66]

Intuitively, I think Rapt is right about this banded/distributed arrangement. I wouldn't do it that way. What are the reasons it is common practice in the US? You wouldn't arrange deformed bars that way, so why posttensioning tendons? When the slab wants to span in both directions, you can't force it to work as a one way system.

 

[csd72]

haynewp,
re:"...for EACH direction so you are reinforcing it for that load twice but this is required."

Fundamentally it is no different than a slab supported on beams on 4 sides. except the beams would take the moment in one direction and the slab in the other. The only reason for the different analysis is the difference in relative stiffness.

csd

 

[haynewp]

csd,

Yes that is right. The load is taken 100% in each direction for both a 2 way flat plate and 2 way slab on beam case. Or even a one way slab and beam system. Just like steel roof joists take the load to girders then the girders take the load to the columns.

For a 2 way flat slab without beams the slab itself takes the load in one direction then in the other.

 

[csd72]

haynewp,

not trying to correct you, just trying to make it clearer for anyone that doesnt understand that fact.

csd

 

[JAE]

Good replies.....and rapt - whew...what a dissertation. Appreciate the time it took to do it.

As far as load being taken twice...I was using that description to make the point that it seems that SOME of the load is counted twice (and thus there is some level of redundancy in the EFM)...probably not 100% and 100% but some level of duplication.

I seem to see gsmith22's point about the slab not being fully connected/supported by the column but by the orthoganal slab.

 

[gsmith22]

wow. go away for a few days and there is alot to read!

rapt, very nice summary. I was under the impression from your first post that you were bashing the EFM and/or finite element. However, now I see that your only concern is the use of banded/distributed tendons and the fact that their layout does not match the elastic response of the slab. I can very much concour with most of your thoughts and I too had similar concerns when I first started design with PT. The one difference that maybe we are all forgetting is that a PT slab is under compression in addition to bending moments. Hopefully you are using an Mc/I+P/A to analyze the slab when talking about first cracking as that P/A can have a large effect. Due to the compression, you will most likely not have tension at the top of your slab away from columns and a large portion of the slab will be uncracked and thus stiffer than a similarly designed conventional slab-also required by ACI due to stress limitations. But assuming you have done this, the following may be of help.

Banded/Distributed. As far as I can tell/have read, most of the PT design for buildings in the US was started through contractors experimenting and not engineers designing or professors teaching. As such, they developed methods that were easy to build. The engineering industry followed their lead istead of the other way around. The banded/distributed layout of tendons is a contractor favorite because it almost completely eliminates any weaving of tendons. Basically, place all the banded tendons close to column lines first, then place all the uniform tendons. ACI has done numerous research on the use of different tendon layouts and has concluded that there is no significant difference in the distribution of compression into the slab via the tendons whether the tendons are banded, distributed, or some mix of the two. Compression is basically uniform in the slab away from anchorages.

Cracking. If we can assume the ACI is correct and that all compression distributes equally into the slab, then the only question here is why the use of full strip width for moment design. This is clearly conservative from the standpoint of the "middle strip" as it will have lower moments elastically than a neighboring "column strip". Throw in the compression via the tendons and I doubt you have any problem with eliminating top bars at the support line "middle strip." So what then happens at "column strip"? Well limiting the max stress to 6*SQRT(f'c) certainly helps here as well as being forced to provide a minimum amount of top bars at the column (ACI's way of recognizing the flaws in their analysis?) but ultimatly, you are somewhat right in that the stress at the columns is probably higher than being calculated since the column strip beam was artifically too wide.

I haven't really personally worried about it but that maybe because most things I have designed 2-way flat plate PT have been residential with low live load (40psf and reducible) that is rarely ever achieved in reality. I think I recall much higher live loads being talked about previously (and probably unreducible) so the stresses are probably much closer to the limits than my buildings.

Conclusions. If you are near 6*SQRT(f'c) for negative moment stresses, clearly recognize that the true stress right at the column face maybe much higher and maybe add some extra bars to reinforce it if it bothers you. The true deflecton calculation will probably be worse than a completely uncracked slab if you are near stress limits but I still would maintain that a large portion of the slab will be uncracked. The moment of inertia doesn't immediately drop as soon as a single crack develops, but there is a smoothing of the stress/deflection curve-the reason for Ie calculations in Chapter 9 of ACI. It is always best to recognize when a code has simplified a much more complex system and as you near code limits, pay attention to some of the assumptions of the code-which it appears that rapt has to his credit.

 

[rapt]

gsmith22,

Yes the axial prestress sort of distributes evenly in a flat plate (except for membrane action, and not with T beams/band beams) but this stress is normally much lower than the bending stresses which do distribute unevenly across a slab panel width. You cannot base the distribution of the moments on the distribution of the P/A which as some "experts" have suggested previously in print.

Yes, the early designs using this method used much lower stress levels so they were ok. Now people want to do partial prestressed design (like we have in the Australia for 30 years). To do this, you have to look at the stress concentrations, not averages, and put the steel where the cracks are.

I have seen people justifying slabs with 30-50kPa live load (600 - 900 psf) and with drop panles using banded distributed tendons and average moment design. Also heavily loaded transfer slabs. Their results are stupid and it is all because they read ACI and PTI documents and get the impression from these that this is how a PT slab actually works rather than it being a simplification with limited applicability.

Deflections do increase significantly on the appearance of the first crack. Branson's formula says that they don't but all approximations have their limitations and this is the main limitation of Bransons formula. It is unconservative at the first crack and for lightly stressed/cracked members. That is why ACXI is the only code that uses it in its original form.

 

[rapt]

gsmith22,

The other area that worries me with all of this is designs for floors with variable concrete sections, either drop panels or beams and also slabs with large concentrated loads.

Designers are treating both of these like lightly loaded flat plates. They are including tendons in slabs a long way fro the changes in depth as having the same effective depth as the tendons in the area of the change in depth, eg tendons in slabs parallel to beams are included in the beam section for design and also include a very wide flange. It is garbage but they are doing it.

Same with drop panel slabs where the tendons between the drop panels are treated as if they are over the drop panels.

The actual capacities of these slabs are significantly lower than the designers think. And they are encouraged to do it by some software developers who simply do not understand design no matter how much they put their names up in lights.

With large concentrated loads, they are treating the design like a normal positive moment area for a uniforn load design but it is actually more like a negative moment area in the way it acts and the tendons and reinforcement have to be arranged accordingly and the design needs to consider this. Basic banded/distributed and "averaged moments" just does not work with this type of design.

 

[gsmith22]

rapt,
I realy don't have any problem with what you are suggesting here. Alot of it makes perfect sense and should be checked and not just ignored.

I would offer this though. Codes are written to be conservative for the average building. What you appear to be designing on some sort of regular basis (Slabs supporting 600-900 psf) are by no means average and in fact I would suggest you are designing something that probably few other people in the world are designing and as such should be looked at with a critical eye. The code was not written for your building and while these loads may seem "regular" to you, I would suggest are far from regular to everyone else and probably the code writers. I would argue that most pT flat plate two-way slabs are used for loads in the 40-150 psf range. Hell, the building code doesn't even list live loads larger than 250psf and that is for supporting truck loading.

To be honest, I am slightly shocked that you would even consider using a flat plate (PT or non PT) for the loading being considered. I certainly can understand how a partial prestress would have negligible effect on your slabs-I haven't put numbers to it, but a PT slab with service live load of 600-900psf is probably akin to a non-pt slab with srevice live load of 300 psf or more of bending stress. I would guess that you must have slabs measured in feet thick (or centimeter) instead of inches (or mm) based on keeping stresses low at the columns while the center of the bays, there is relatively very low stress. If I had that kind of load, I would be using one way slab and beams (PT or non PT) because at those stress levels, it would seem as though a significant amount of concrete and rebar would be wasted within the interior of a bay where the slab doesn't have to be so thick. In fact, you seem to be suggesting you need this type of layout anyway given your drop panels, thickened slab beams, etc.

 

[rapt]

gsmith22,

I am not designing them. They are cases I see quite often around the world and they are fairly common in Europe, Middle East, Asia and Australia.

I am just trying to let people know that they cannot believe everything they read and are told by software salesmen and that is calculated by software, garbage -> garbage.

 

[hokie66]

Rapt is correct in that in other countries, floors are often designed for heavier loading than in the US. For instance,in Australia many supermarkets are in shopping malls on the upper levels, and the loading docks and storage areas in these stores are typically designed for 300 to 400 psf (stacks of cans of peas are heavy). Also, many tranfer floors between the parking levels and commercial or residential space above are designed with flat plates 2 to 4 ft thick.

 

[gsmith22]

you learn something new everyday! In my experience, when ever I had a transfer slab or loading of those high magnitudes, I used one-way beam and slabs. It provides a significantly better load path (especially for a transfer slab with column point loads), doesn't waste so much concrete between the beams (at some point repetetive formwork with beams is as cheap as flat formwork with a slab so thick), and as you can attest to, aren't relying on all of these simplified code design methodologies. 2' to 4' thick is just insane for a flat plate. What are the spans? You probably could of had 2'Wx2.5'D beams with 8" slabs between. Computers are only helpful if you understand the math behind the algoriths and can do it by hand without the computer. Adapt isn't signing and sealing any drawings!

 

[hokie66]

The transfer floors I am talking about are buildings where the architect designs everything above the podium without regard for supporting conditions below. So the columns or walls above are more or less randomly located, while the columns below are controlled by carparking, but the carparking itself is often irregular. I couldn't agree more that beams and slabs are a better system, but unfortunately when nothing lines up, beams don't work very well.

A typical example would be a 15 storey residential building over 3 levels of carparking. The spans are usually in the range of 12 to 15 times the plate thickness.

There are some offsetting advantages: formwork simplication, less excavation, more attractive soffit with better lighting, simpler plumbing are a few.